Answer:
(20,-4)
Step-by-step explanation:
We are given;
One end point as (2,5)
Point of division as (10,1)
The ratio of division as 4:5
We are required to calculate the other endpoint.
Assuming the other endpoint is (x,y)
Using the ratio theorem
If the unknown endpoint is the last point on the line segment;
Then;
[tex]\left[\begin{array}{ccc}10\\1\end{array}\right][/tex]=[tex]\frac{4}{5} \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]+[tex]\frac{5}{9}\left[\begin{array}{ccc}2\\5\end{array}\right][/tex]
Therefore; solving the equation;
[tex]10=\frac{4}{9}x+\frac{10}{9}[/tex]
solving for x
x = 20
Also
[tex]1=\frac{4}{9}y+\frac{25}{9}[/tex]
solving for y
y= -4
Therefore,
the coordinates of the end point are (20,-4)
